Quasars (abbreviation for of "quasi-stellar radio source") or QSOs (quasi-stellar object) are generally identified as very bright star-like objects with 'large' redshifts and large variations in luminosity on time-scales of months to days and even hours. These 'large' emission-line redshifts are on a non-thermal continuum, i.e. the spectrum of radiation from the source cannot be described as originating from the thermal energy of the gases in its atmosphere, such as is found in normalstars as our Sun.
According to J.Hartnett the terms 'large' and 'star-like' are however never adequately defined and there have been already identified many lower-redshift QSOs, some with fuzz (i.e. stars) around their central nuclei. This causes problems for usual interpretation as fuzz should not be visible at the cosmological distances indicated by their redshifts and the Hubble Law. The standard belief of modern astrophysics is that quasars are systems of accreted matter around super-massive black holes and their redshifts are cosmological in origin, i.e. related to distance. The high values of these redshifts should indicate the vast cosmological distances from Earth.
Many quasars however indicate the association to galaxies which do not have large redshifts. Some astronomers thus question whether the large redshifts of quasars is truly related to distance (i.e. cosmological redshift), a fortiori since the inference of large distances imposes a number of contradictory conclusions, including:

Massive luminosity: Most QSOs have large redshifts and if interpreted as a measure of distance according to the Hubble Law, that would place them with unreasonably high luminosities ~100 times those of normal galaxies. These facts led to what was called the Comptom paradox or inverse-Comptom catastrophe, a physically impossible state due to the very high radiation densities in these sources.

Excessively rapid rotation

Expansion of jets at greater than the speed of light: Radio-astronomers have measured outward motions of structures (jets) within QSOs over several years. On some occasions these measurements suggested the jet components should be moving at 10 times the speed of light. There have been many weak arguments presented to counter this assertions which would become unnecessary if the intrinsic component in the redshift (see below) would be assumed instead of preserving the conventional distance-based redshift interpretation for quasars.

The alternative proposition is that not all redshifts value of quasars is given by cosmological redshift (i.e. related to distance) but there might be a substantial intrinsic component involved which cannot be explained by cosmological expansion, gravitational or Doppler Effects. It has been suggested that intrinsic redshift component is the result of the initial zero inertial-mass of newly created matter that has been ejected from the cores of active galactic nuclei. This would mean that quasars might not be really so far away, and thus Hubble Law does not apply onto quasars and we need to be careful in its application.[note 1] This may indicate the serious flaw in the Big Bang paradigm[1] which postulates the creation of all matter in the universe at the early stages of the hot Big Bang and then relies on space expansion as described by Hubble Law for its distribution.[2]

References

↑Michail S. Turner. Dark Matter, Dark Energy and Inflation: The Big Mysteries of Cosmology 0h:07min:41sec/1h:11min:39sec. Arizona connection, Lectures series. Retrieved on 2012-10-15. “Ordinary matter: From quarks to us:
Implications of Hubble’s discovery was: In the beginning the universe was small and it got bigger and evolved, and so there was a big bang. Penzias and Wilson had discovered that there are billions of microwave photons filling the universe for every atom and this is the heat-leftover from the big bang and that big bang was a hot big bang. And that changes everything because in the beginning there was really hot...it was hotter than in hell…When you heat something up you reduce it to its basic elements and that means that in the beginning the universe was a primordial soup. And so what is primordial soup made of? In 1970s we figured out what the basic pieces what the basic building blocks of matter are – and those are called quarks …The neutrons and protons were made of smaller entities called quarks, … combining that with fact that the universe was hot at the beginning we can figure out what that primordial soup was…I’m going to show you the full-scale model of the entire universe that we see today, what it would look like at the beginning … everything that we can see, 100 billion galaxies, all fit into this soup … and they were reduced to their quark constituents. …We can now reconstruct the history of the universe from quark soup to us…When the universe was younger than one one-hundred thousandth of the second and as we follow it through it’s expanding, it’s cooling, layer upon layer of structure is building up. And so when it was about one one hundred thousandth of the second old, it was cool enough for neutrons and protons to form. And as it cooled, it became cool enough for the neutrons and protons to come together and make the nuclei of the lightest elements in the periodic table and that happened when the universe was a few seconds old. When the universe was a few seconds old there was a nuclear reactor and that nuclear reactor made a lot of helium, made little bit of deuterium, made a Helium3-that’s a light form of helium and it made a tiny amount of lithium…The rest of the elements in periodic table were made in stars and … stars made the rest of the periodic table.”